I try hard to be less biased against “weird” ideas (somewhat self serving since I have weird ideas), so I will bite a bullet and say that lawsuit gambling is a fabulous idea:
[L]et people risk their lawsuits, double or nothing. After that damaging party, you would write out a simple complaint, including who hurt you when and how, and then take this complaint to the official lawsuit randomizing office, who would then randomly declare it worthless (50% chance) or double it (50% chance). If your suit were doubled, and you took it to court and won, so that the court said your neighbor caused you $X in damages, they would really owe you twice $X. And if you gambled and lost your neighbor would get a record of this, to defend against your trying to sue again over the same complaint.
More generally, you could keep doubling your suit so that it is worth any power of two times $X, or nothing. So if you gambled your $50 party suit ten times, for a factor of 1024, then 1023 times out of 1024, you’d get nothing. But that last time you’d get a suit worth $51,200 if you won. Then it would be worth your while to actually go to court to win it. And since your neighbor would know this, they should want to settle rather than go to court. And since they know, before you gamble your suit, that this is a possibility, they should be willing to settle up front for near the $50.
The critical mechanism here is that litigants only pay the costs of conducting a lawsuit if their lawsuit is selected, and in this case their lawsuit is worth much more than it used to be.
I suspect that such lawsuits would probably need to have somewhat different rules than normal lawsuits, but I don’t know in what way. I will only add that I think lawsuit gambling would do a good job of replacing or augmenting lots of consumer and worker protection mechanisms such as class action lawsuits.